Stochastic modeling of multidimensional particle properties with parametric copulas for the investigation of microstructure effects on the fractionation of fine particle system

在这个项目中，SPP 2045第一个资助期开发的数学分析和建模技术将应用于SPP 2045合作伙伴研究的粒子系统的图像数据和测量。此外，还进一步开发了量化分离成功以及多维粒子特征与分离相关物理参数之间关系的方法。此外，建立了一个立体预测模型，通过粒子系统从二维剖面中表征三维粒子。重点做好以下工作。在第一个资助期开发的方法用于从CT图像数据中提取颗粒，用于颗粒特征的多元分布的参数化建模，用于从CT数据中表征复合颗粒中的材料，以及用于量化分离成功，这些方法应用于进一步的颗粒系统并在必要时进行修改。为此，将从CT数据中自动提取颗粒以及随后对颗粒的多变量特征分布进行建模的工作流程应用于分离过程应用前后的颗粒系统。这将CT图像数据的（困难的）直接比较减少为原料和产品颗粒特性分布的比较。随后，确定分离成功的指标，如纯度和收率，以分析和比较分离方法的质量。另一个项目目标是利用随机3D粒子模型，即通过生成描述粒子形状和内部结构的“数字双胞胎”，量化粒子特性和分离成功之间的关系。此外，这些模型允许生成范围广泛的具有不同特征分布的虚拟但现实的粒子。这些虚拟粒子将通过粒子数据库提供给spp2045的合作伙伴小组，这样合作伙伴就可以将它们作为沉积和流动过程数值模拟的输入。通过将模拟结果与进料颗粒特性的多元分布相关联，确定颗粒特性与分离成功之间的关系。此外，建立了一个立体预测模型，该模型通过粒子系统确定二维切片（例如通过扫描电镜测量获得）三维粒子特征的多元分布。为此，将上述随机（单）粒子模型扩展为空间分散的粒子系统模型。通过生成大量的虚拟三维粒子系统来训练神经网络，该神经网络可以从所考虑的粒子系统的二维部分中表征三维粒子。

In this project, the mathematical analysis and modeling techniques developed in the first funding period of the SPP 2045 will be applied on image data and measurements of particle systems which are investigated by the partners within SPP 2045. In addition, the methods are further developed, which quantify the separation success and the relationship between multidimensional particle characteristics and separation-relevant physical parameters. Furthermore, a stereological prediction model is developed to characterize 3D particles from 2D sections through the particle systems. In particular, the following tasks will be addressed. The methods developed in the first funding period for extracting particles from CT image data, for parametric modeling of multivariate distributions of particle characteristics, for characterizing the materials within composite-particles from CT data, and for quantifying the separation success, are applied to further particle systems and modified if necessary. For this purpose, the workflow, consisting of the automated extraction of particles from CT data and the subsequent modeling of multivariate feature distributions of the particles, is applied to particle systems before and after the application of separation processes. This reduces the (difficult) direct comparison of CT image data to the comparison of distributions of particle characteristics of the feed material and the product. Subsequently, measures for the separation success, such as purity and yield, are determined to analyze and compare the quality of the separation methods. Another project goal is to quantify the relationship between particle properties and separation success using stochastic 3D particle models, i.e., by generating "digital twins" which describe the shape and internal structure of the particles. Furthermore, these models allow the generation of a wide range of virtual but realistic particles with different feature distributions. These virtual particles will be made available to the partner groups of SPP 2045 via a particle database, such that the partners can use them as input for numerical simulations of sedimentation and flow processes. By correlating the simulation results with multivariate distributions of characteristics of the feed particles, relationships between particle properties and separation success will be determined. In addition, a stereological prediction model is developed, which determines multivariate distributions of characteristics of 3D particles from 2D slices (gained e.g. by SEM measurements) through the particle system. For this purpose, the above-mentioned stochastic (single) particle models are extended to a model for spatially dispersed particle systems. By generating a large number of virtual 3D particle systems neural networks are trained, which can characterize the 3D particles from 2D sections of the considered particle system.